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arXiv:2007.14131 · Physical Review A

Dynamical Zeeman resonance in spin-orbit-coupled spin-1 Bose gases

Jingtao Fan, Gang Chen, Suotang Jia

Published Dec 7, 2020• 3 citations
arXivHTMLPDF

Abstract

We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.

DOI
10.1103/physreva.102.063311

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We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.
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We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing-wave phase or plane-wave phase when the strength of the Zeeman field is below a critical value related to the strength of spin-orbit coupling. The Zeeman field can induce a phase transition between standing-wave and plane-wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner: the linear Zeeman effect magnetizes the standing-wave phase along the direction of the magnetic field, but the quadratic Zeeman effect demagnetizes the plane-wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.
We propose a mechanism to realize nontrivial spin dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate by abruptly shaking the harmonic trap. Continuously varying the shaking strength, it is found that the Bose-Einstein condensate may exhibit exotic nonequilibrium spin dynamics. Specifically, at some special values of the shaking strength, the time-averaged spin polarization shows sharp resonant peaks, whereas it tends to be zero at any other positions. Furthermore, the spacings between any two nearest peaks depend only on the system parameters and are thus identical to each other. By simplifying this time-dependent system to an exactly solvable ``quantum quench'' model, we show that the essential physics behind the exotic spin dynamics comes from periodic suppressing and enhancing of the out-of-phase interference. It is further shown that the presented physical picture persists under weak atomic interactions. This work may shed light on the ongoing research of spin-based quantum control and quantum information.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
I will discuss the spin dynamics of two magnetic atoms trapped in an external trap. Assuming that initially the atoms are in their orbital ground state I will discuss in details all possible elementary processes of spin flipping. Dipole-dipole interactions couple spin degrees of freedom of the two particles to their quantized orbital motion. Because of conservation of the total angular momentum if a magnetization of the system changes the system acquires an orbital angular momentum and atoms circulate around the center of the trap. I show that spin dynamics driven by dipolar interactions is possible only when the energies of the initial and the final sates are equal. In a case of weak magnetic moments of atoms this condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. I will illustrate the resonant dynamics comparing the theoretical predictions to some results of experiments on Chromium atoms.
We study the collective excitation spectrum of a Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional harmonic trap while varying either the Raman coupling or quadratic Zeeman field strength by using the Bogoliubov approach. A few low-lying modes, which can be used to delineate the phase boundaries, are identified by exciting them with suitable perturbations. We also investigate the coarsening dynamics of a homogeneous quasi-two-dimensional spin-orbit-coupled spin-1 condensate by quenching from the zero momentum into the plane wave phase through a sudden change in Raman coupling or quadratic Zeeman field strength. We demonstrate that the correlation function of the order parameter displays dynamic scaling during the late-time dynamics, allowing us to determine the dynamic critical exponent.